Discrete Mechanical Systems: Second Order Modelling and Identification

We exploit a new discretization technique of the Lagrange equations of motion of a mechanical system, derived from the concept of variational integrators introduced by Veselov and further developed by J.Marsden an co-workers, for the identification of linear mechanical systems. This discretization technique preserves the physical meaning of the model parameters and, unlike the usual discretization procedures by zero-order-hold, leads to simple and well-conditioned transformation formulas for the recovery of the continuous time parameters from the discretized model. We discuss the identification of these discrete models starting from measured data and compare the corresponding continuous-time parameters with those obtained by standard state-space based algorithms from the literature.